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# Distributions

 Different Distributions Uniform (flat) distribution: 6 sided dice simulation and a 6 to 30 sided dice Triangular distribution Sum of Two 6 sided simulation (horse race) Drawing Distributions, mix and match, Popcorn sound distribution How greater data and narrower intervals approximates a bell shape curve. Overview of the normal distribution curve. Interactive web site java simulation www.shodor.org Theta (new & old & workbook) Ex24.01 Normal Distribution Introduction Calculation of the mean and standard deviation. Normal Distribution introduction and overview. The effect of changing the mean and/or standard deviation Standard Dev: Class notes | Blank notes Normal: Class notes | Blank notes Theta (new & old & workbook) Ex24.02 and Ex24.03

# Histograph & Distributions

### If a set of data is grouped and displayed using a histograph a distribution of the data is produced

Even distribution

No central tendancy
Skewed distribution

More data at lower values
Two regions of distribution

Two data bunches: around 20 and 40

### Usually data sets display central tendancy (most data around some value) and a spread either side of this value. One measure of central tendancy is the mean µ One measure of spread is the standard deviation σ

A histograph or a set of 500 data values

With a population mean µ=10 and standard deviation of σ = 5
Reducing the interval width on the histograph

Note: all the areas add to a total of 1.0
And reducing the interval width more

Note: all the areas still add to a total of 1.0
The histograph can be approximated with the NORMAL DISTRIBUTION curve
There is a central tendancy and a symmetrical spread either side
A NORMAL DISTRIBUTION curve

With mean µ=10 and standard deviation of σ = 5

Note: the area under the graph equals 1.0